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Academic literature on the topic 'Timescale separation system dynamics'
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Journal articles on the topic "Timescale separation system dynamics"
1
Williamson, Mark S., Sebastian Bathiany, and Timothy M. Lenton. "Early warning signals of tipping points in periodically forced systems." Earth System Dynamics 7, no. 2 (2016): 313–26. http://dx.doi.org/10.5194/esd-7-313-2016.
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Abstract. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.
2
Wu, Weijun, Andrew E. Sifain, Courtney A. Delpo, and Gregory D. Scholes. "Polariton enhanced free charge carrier generation in donor–acceptor cavity systems by a second-hybridization mechanism." Journal of Chemical Physics 157, no. 16 (2022): 161102. http://dx.doi.org/10.1063/5.0122497.
Full textAbstract:
Cavity quantum electrodynamics has been studied as a potential approach to modify free charge carrier generation in donor–acceptor heterojunctions because of the delocalization and controllable energy level properties of hybridized light–matter states known as polaritons. However, in many experimental systems, cavity coupling decreases charge separation. Here, we theoretically study the quantum dynamics of a coherent and dissipative donor–acceptor cavity system, to investigate the dynamical mechanism and further discover the conditions under which polaritons may enhance free charge carrier generation. We use open quantum system methods based on single-pulse pumping to find that polaritons have the potential to connect excitonic states and charge separated states, further enhancing free charge generation on an ultrafast timescale of several hundred femtoseconds. The mechanism involves polaritons with optimal energy levels that allow the exciton to overcome the high Coulomb barrier induced by electron–hole attraction. Moreover, we propose that a second-hybridization between a polariton state and dark states with similar energy enables the formation of the hybrid charge separated states that are optically active. These two mechanisms lead to a maximum of 50% enhancement of free charge carrier generation on a short timescale. However, our simulation reveals that on the longer timescale of picoseconds, internal conversion and cavity loss dominate and suppress free charge carrier generation, reproducing the experimental results. Thus, our work shows that polaritons can affect the charge separation mechanism and promote free charge carrier generation efficiency, but predominantly on a short timescale after photoexcitation.
3
Webber, S., and M. R. Jeffrey. "Loss of Determinacy at Small Scales, with Application to Multiple Timescale and Nonsmooth Dynamics." International Journal of Bifurcation and Chaos 31, no. 03 (2021): 2150041. http://dx.doi.org/10.1142/s0218127421500413.
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A singularity is described that creates a forward time loss of determinacy in a two-timescale system, in the limit where the timescale separation is large. We describe how the situation can arise in a dynamical system of two fast variables and three slow variables or parameters, with weakly coupling between the fast variables. A wide set of initial conditions enters the [Formula: see text]-neighborhood of the singularity, and explodes back out of it to fill a large region of phase space, all in finite time. The scenario has particular significance in the application to piecewise-smooth systems, where it arises in the blow up of dynamics at a discontinuity and is followed by abrupt recollapse of solutions to “hide” the loss of determinacy, and yet leave behind a remnant of it in the global dynamics. This constitutes a generalization of a “micro-slip” phenomenon found recently in spring-coupled blocks, whereby coupled oscillators undergo unpredictable stick-slip-stick sequences instigated by a higher codimension form of the singularity. The indeterminacy is localized to brief slips events, but remains evident in the indeterminate sequencing of near-simultaneous slips of multiple blocks.
4
Costa, Antonio C., Tosif Ahamed, David Jordan, and Greg J. Stephens. "Maximally predictive states: From partial observations to long timescales." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 2 (2023): 023136. http://dx.doi.org/10.1063/5.0129398.
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Isolating slower dynamics from fast fluctuations has proven remarkably powerful, but how do we proceed from partial observations of dynamical systems for which we lack underlying equations? Here, we construct maximally predictive states by concatenating measurements in time, partitioning the resulting sequences using maximum entropy, and choosing the sequence length to maximize short-time predictive information. Transitions between these states yield a simple approximation of the transfer operator, which we use to reveal timescale separation and long-lived collective modes through the operator spectrum. Applicable to both deterministic and stochastic processes, we illustrate our approach through partial observations of the Lorenz system and the stochastic dynamics of a particle in a double-well potential. We use our transfer operator approach to provide a new estimator of the Kolmogorov–Sinai entropy, which we demonstrate in discrete and continuous-time systems, as well as the movement behavior of the nematode worm C. elegans.
5
Williamson, M. S., S. Bathiany, and T. M. Lenton. "Early warning signals of tipping points in periodically forced systems." Earth System Dynamics Discussions 6, no. 2 (2015): 2243–72. http://dx.doi.org/10.5194/esdd-6-2243-2015.
Full textAbstract:
Abstract. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much recent interest. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we find alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose time scale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. We show that the phase lag and amplification of the system response provide early warning signals, based on a linear dynamics approximation. Furthermore, the power spectrum of the system's time series reveals the generation of harmonics of the forcing period, the size of which are proportional to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.
6
Ha, Sang Wook, and Bong Seok Park. "Disturbance Observer-Based Control for Trajectory Tracking of a Quadrotor." Electronics 9, no. 10 (2020): 1624. http://dx.doi.org/10.3390/electronics9101624.
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This paper presents a new control approach for the trajectory tracking of a quadrotor in the presence of external disturbances. Unlike in previous studies using hierarchical control strategies, a nonlinear controller is designed by introducing new state transformations that can use Euler angles as virtual control inputs. Thus, the proposed method can eliminate the timescale separation assumption of hierarchical control strategies. To estimate the external disturbances involved in the translational and rotational dynamics of the quadrotor, disturbance observers are developed. Using state transformations and estimates of external disturbances, we design a robust nonlinear controller based on the dynamic surface control method. The stability of the closed-loop system is analyzed without separation into two subsystems. From the Lyapunov stability theory, it is proven that all error signals in the closed-loop system are uniformly ultimately bounded and can be made arbitrarily small. Finally, simulation results are presented to demonstrate the performance of the proposed controller.
7
Benavides, Santiago J., Keaton J. Burns, Basile Gallet, and Glenn R. Flierl. "Effective Drag in Rotating, Poorly Conducting Plasma Turbulence." Astrophysical Journal 938, no. 2 (2022): 92. http://dx.doi.org/10.3847/1538-4357/ac9137.
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Abstract Despite the increasing sophistication of numerical models of hot Jupiter atmospheres, the large timescale separation required in simulating the wide range in electrical conductivity between the dayside and nightside has made it difficult to run fully consistent magnetohydrodynamic (MHD) models. This has led to many studies that resort to drag parameterizations of MHD. In this study, we revisit the question of the Lorentz force as an effective drag by running a series of direct numerical simulations of a weakly rotating, poorly conducting flow in the presence of a misaligned, strong background magnetic field. We find that the drag parameterization fails once the timescale associated with the Lorentz force becomes shorter than the dynamical timescale in the system, beyond which the effective drag coefficient remains roughly constant, despite orders-of-magnitude variation in the Lorentz (magnetic) timescale. We offer an improvement to the drag parameterization by considering the relevant asymptotic limit of low conductivity and strong background magnetic field, known as the quasi-static MHD approximation of the Lorentz force. This approximation removes the fast timescale associated with magnetic diffusion, but retains a more complex version of the Lorentz force, which could be utilized in future numerical models of hot Jupiter atmospheric circulation.
8
Lee, Ka Kit, Darren Yi Sern Low, Mei Ling Foo, et al. "Molecular Dynamics Simulation of Nanocellulose-Stabilized Pickering Emulsions." Polymers 13, no. 4 (2021): 668. http://dx.doi.org/10.3390/polym13040668.
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While the economy is rapidly expanding in most emerging countries, issues coupled with a higher population has created foreseeable tension among food, water, and energy. It is crucial for more sustainable valorization of resources, for instance, nanocellulose, to address the core challenges in environmental sustainability. As the complexity of the system evolved, the timescale of project development has increased exponentially. However, research on the design and operation of integrated nanomaterials, along with energy supply, monitoring, and control infrastructure, has seriously lagged. The development cost of new materials can be significantly reduced by utilizing molecular simulation technology in the design of nanostructured materials. To realize its potential, nanocellulose, an amphiphilic biopolymer with the presence of rich -OH and -CH structural groups, was investigated via molecular dynamics simulation to reveal its full potential as Pickering emulsion stabilizer at the molecular level. This work has successfully quantified the Pickering stabilization mechanism profiles by nanocellulose, and the phenomenon could be visualized in three stages, namely the initial homogenous phase, rapid formation of micelles and coalescence, and lastly the thermodynamic equilibrium of the system. It was also observed that the high bead order was always coupled with a high volume of phase separation activities, through a coarse-grained model within 20,000 time steps. The outcome of this work would be helpful to provide an important perspective for the future design and development of nanocellulose-based emulsion products, which cater for food, cosmeceutical, and pharmaceutical industries.
9
Wouters, Jeroen, Stamen Iankov Dolaptchiev, Valerio Lucarini, and Ulrich Achatz. "Parameterization of stochastic multiscale triads." Nonlinear Processes in Geophysics 23, no. 6 (2016): 435–45. http://dx.doi.org/10.5194/npg-23-435-2016.
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Abstract. We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system; we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large timescale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost.
10
Paddon-Row, Michael N. "Superexchange-Mediated Charge Separation and Charge Recombination in Covalently Linked Donor - Bridge - Acceptor Systems." Australian Journal of Chemistry 56, no. 8 (2003): 729. http://dx.doi.org/10.1071/ch02249.
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Evidence is presented in support of the concept that electron transfer (ET) between a pair of chromophores may take place efficiently over large distances (>10 Å) by the mediation of an intervening saturated hydrocarbon medium. For example, ET is found to take place on a sub-nanosecond timescale through saturated norbornylogous bridges greater than 13 Å in length, by a superexchange (through-bond coupling) mechanism. The dependence of the ET dynamics on the bridge length and configuration are consistent with the operation of a superexchange mechanism. The distinction between molecular wire behaviour and superexchange-mediated ET is made. The distance dependence of ET dynamics through different types of bridges—saturated and unsaturated hydrocarbon bridges, proteins, and duplex DNA—is discussed and explained. Strategies for prolonging the lifetimes of charge-separated states are explored and discussed. In general, long-lived charge-separated species have been generated using giant multichromophoric systems in which the charges are separated by large distances, often exceeding 20 Å. In contrast, it is shown that very long-lived charge-separated states, possessing the triplet multiplicity, may be generated using short ‘dwarf’ dyads, in which the charges are less than 6 Å apart. Charge recombination in these species is slowed by the difference in electron spin multiplicity between the charge-separated state and the ground state.